Color rendering index (CRI) is a quantitative measure of the ability of a light source to reproduce the colors of various objects faithfully in comparison with an ideal or natural light source. The CRI system is administered by the International Commission on Illumination (CIE). The CIE selected fifteen test color samples to grade the color properties of a white light source. The first eight test color samples are relatively low saturated colors and are evenly distributed over the complete range of hues. These eight samples are employed to calculate the general color rendering index Ra. The general color rendering index Ra is simply calculated as the average of the first eight color rendering index values, R1-R8. An additional seven samples provide supplementary information about the color rendering properties of the light source; the first four focus on high saturation, and the last three are representative of well-known objects.
A set of color rendering index values, R1-R15, can be calculated for a particular correlated color temperature (CCT) by comparing the spectral response of a light source against that of each test color sample, respectively. The calculation consists of taking the differences ΔEj, between the spectral power distribution of a test color sample and the spectral power distribution of the light source under test at any number of equally spaced wavelengths over the range of wavelengths under test. Based on these differences, each specific color rendering index value is calculated as follows:
                              R          i                =                              ∑                          j              =              1                        N                    ⁢                                    100              -                              4.6                ⁢                                                                  ⁢                Δ                ⁢                                                                  ⁢                                  E                  j                                                      N                                              (        1        )            
The test color samples associated with the various CRI indices are designed such that certain ideal or natural light sources should achieve a CRI value of 100 for each index. For example, below 5,000 Kelvin, the blackbody radiator is taken as the ideal light source. Thus, a blackbody radiator below 5,000 Kelvin has a CRI of 100 for each specific CRI value. Incandescent lamps have a CRI rating approaching 100 as they can be constructed to be a very close approximation of a blackbody radiator. Light sources of limited spectral power distribution, such as arc lamps or light emitting diodes (LEDs) typically exhibit very low CRI values. In general, illumination sources achieving high CRI values are desirable as they offer brilliant color rendering of objects colored across the visible spectrum. A light source that incorporates LEDs and has high CRI values is desired.